Stress–Strain & Hooke’s Law
This lab shows a qualitative engineering stress–strain curve for a ductile metal: σ = Eε in the elastic region until yield, an optional yield plateau, linear strain hardening to the ultimate tensile strength, then a drop in engineering stress during necking until fracture. It is a teaching cartoon, not a calibrated material model.
Who it's for: Intro mechanics of materials and solid mechanics; vocabulary for elastic limit, yield, ultimate, and ductility.
Key terms
- Young’s modulus
- yield stress
- ultimate tensile strength
- necking
- fracture strain
- Hooke’s law
How it works
A qualitative engineering stress–strain curve for a ductile metal: in the elastic region stress is proportional to strain (Hooke’s law, σ = Eε). Beyond the yield point the material flows (here shown as a short plateau), then strain hardening raises stress to the ultimate tensile strength. After the ultimate point, necking makes the engineering stress drop until fracture. Numbers are for illustration — real curves depend on alloy, temperature, and strain rate.
Key equations
Elastic: σ = Eε, ε_y = σ_y/E
Then: yield plateau → hardening to σ_u → necking → σ → 0 at ε_f
Frequently asked questions
- Why does stress drop after the ultimate point?
- The graph uses engineering stress (force divided by original area). During necking the true cross-section shrinks faster than the force drops, so engineering stress typically falls even though true stress may still rise.
More from Engineering
Other simulators in this category — or see all 12.
Quadcopter 2D (Pitch)
Side view: two rotors, PD on thrust split vs pitch — whiteboard quad slice.
Watt Governor (schematic)
Flyballs and sleeve vs RPM; steam throttle gap — speed feedback cartoon.
Logic Gate Simulator
AND, OR, NOT, NAND, XOR. Drag, drop, connect, see output.
Truth Table Generator
Build a circuit, auto-generate the truth table.
Bridge Builder
Place beams and joints. Apply load. See stress distribution.
Gear Train
Connect gears, adjust teeth count, see speed and torque ratios.